Can someone pls help

Traces of surface x2 + y2 − z2 = 1. Determine the equation for the family of traces in x = n.

pickupchik [31]

Answer:

$\mathbf{y^2 -z^2 =1- n^2}$

Step-by-step explanation:

Give that:

the surface equation is $x^2 +y^2 -z^2 =1$

from the family of traces in x = n given that $x^2 +y^2 -z^2 =1$ , the equation can be represented as :

$n^2 +y^2 -z^2 =1$

$\mathbf{y^2 -z^2 =1- n^2}$

This represents a family of hyperbola for all values of n expects that n = ± 1

So, if n = ± 1,

Then

$y^2 - z^2 = 0$

(y-z) (y+z) = 0

y = ± z

So, for n = ± 1, it is a pair of line for y = z, y = -z

6 0

3 years ago

A piece of carpet is 8 feet wide and 12 feet long the carpet needs to be reduced by a scale farctor so that the reduced carpet i

Murljashka [212]

Answer: 6 ft ^ 2

Step-by-step explanation:

We have been given that a piece of carpet is 8 feet wide and 12 feet long. The carpet needs to be reduced by a scale factor so that the reduced carpet is 2 feet wide.

First of all, let us find the scale factor by which the width of the carpet has been reduced.

Original width of carpet x scale factor = 12

Dividing both sides by 8 feet we will get:

8 feet x Scale factor/8 ft = 2/8 ft

Scale Factor = 1/4

Let us find the length of carpet after reduced by a scale factor of 1/4.

Length of the carpet after reducing a factor of 1/4=12 ft x 1/4

Length of the carpet after reducing a factor of 1/4=3 ft.

Now we will multiply the reduced length and width of the carpet to find the area of reduced carpet.

Area of reduced carpet = 2 ft x 3 ft

Area of reduced carpet = 6 ft

Therefore, the area of reduced carpet is 6 square feet.

5 0

3 years ago

The equation of a line is y-4=3(x+2),which of the following is a point on the line?

Greeley [361]

After you re-arrange the equation, you'll find out that you got y=3x+6....okay, this equation is a linear equation, you can use y=mx+b {where m=3, and b=6}. then to find the co-ordinate of (x,y) which is the point, substitute 1,2,3,4.... for x in 'y=3x+6' to figure out the co-ordinate of y.

answer: (1,14), (2,16), (3,19), (4,22)

8 0

3 years ago

2x+5y=46 5x+3y=58 what are the x and y values

nadya68 [22]

(X,y)=(8,6)
Step by step explanation:

3 0

3 years ago

. Imagine a game of 3 players where exactly one player wins in the end and all players have equal chances of being the winner. T

lbvjy [14]

Answer:

5/9

Step-by-step explanation:

Number of players = 3

number of times game is repeated = 4

P( any person wins a game ) = 1/3

P ( any person does not win a game ) = 1 - 1/3 = 2/3

P ( any person wins no game in 4 attempts ) = ( 2/3 )^4 = 16/81

Note : each player has equal chance of winning

Find the probability that there is at least one person who wins no games

lets represent the probability of each player not wining a game with alphabet A

A1 = player 1 wins no game

A2 = player 2 wins no game

A3 = players 3 wins no game

Applying the inclusion-exclusion formula

P( A1 ∪ A2 U A3 ) = P(A1 ) + P(A2) + P(A3) - P( A1 ∩ A2 ) - P( A2 ∩ A3 ) - P( A1 ∩ A3 ) + P( A1 ∩ A2 ∩ A3 )

where

P( A1 ∩ A2 ) = P( A1 wins all games )

P ( A1 wins all games in 4 attempts ) = ( 1/3 )^4 = 1/81

P( A1 ∩ A2 ∩ A3 ) = P ( no players wins any game in 4 attempts ) = 0

Hence

P( A1 ∪ A2 U A3 ) = 16/81 + 16/81 + 16/81 - 1/81 - 1/81 - 1/81 - 0 = 5/9

6 0

3 years ago

Can someone pls help​

Can someone pls help